Details

sample260.0ms

Algorithm

intervals

Results

199.0ms	90×	body	80	nan
25.0ms	279×	body	80	valid

simplify272.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	35	18
1	66	18
2	116	18
3	144	18
4	159	18
5	161	18
6	161	18

prune6.0ms

Filtered

1 candidates to 0 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 21.4b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b b) (* (* 4.0 a) c))
1.4b	(- (* b b) (* (* 4.0 a) c))
23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 54

Calls

4 calls:

3.0ms	(- (* b b) (* (* 4.0 a) c))
3.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* (* 4.0 a) c))
15.0ms	(- (* b b) (* (* 4.0 a) c))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify84.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (77.0ms)

Iter	Nodes	Cost
0	147	474
1	570	446
2	2550	444
3	5001	442

prune166.0ms

Filtered

66 candidates to 50 candidates (24.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	59	7	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	7	67

Merged error: 7.8b

Counts

67 → 7

localize25.0ms

Local error

Found 4 expressions with local error:

12.2b	(- (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div`
4×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `neg-log` `difference-of-squares`

Counts

4 → 60

Calls

4 calls:

4.0ms	(- (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(- (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify108.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (100.0ms)

Iter	Nodes	Cost
0	221	725
1	823	631
2	3496	612
3	5001	592

prune218.0ms

Filtered

72 candidates to 60 candidates (16.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	69	3	72
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	72	7	79

Merged error: 7.8b

Counts

79 → 7

localize26.0ms

Local error

Found 4 expressions with local error:

9.0b	(+ (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div`
4×	`add-exp-log` `add-cbrt-cube`
3×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`
2×	`sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `flip3-+` `neg-log` `flip-+`

Counts

4 → 58

Calls

4 calls:

4.0ms	(+ (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(+ (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify114.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (107.0ms)

Iter	Nodes	Cost
0	227	677
1	876	574
2	3665	562
3	5003	558

prune206.0ms

Filtered

70 candidates to 59 candidates (15.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	68	2	70
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	71	6	77

Merged error: 7.8b

Counts

77 → 6

localize31.0ms

Local error

Found 4 expressions with local error:

23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `flip--` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series62.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify68.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (62.0ms)

Iter	Nodes	Cost
0	127	540
1	454	520
2	1936	516
3	5001	512

prune420.0ms

Filtered

72 candidates to 60 candidates (16.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	72	6	78

Merged error: 7.8b

Counts

78 → 6

regimes254.0ms

Accuracy

90.1% (1.3b remaining)

Error of 9.3b against oracle of 8.0b and baseline of 21.2b

bsearch73.0ms

Steps

Iters	Range		Point
11	60996.03093204275	8.466559853303024e+24	7.468459654509688e+19
5	-1.9379795889221602e+105	-7.097887949638186e+104	-1.8599256214070248e+105

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	58
1	49	58

end0.0ms

sample1.4s

Algorithm

intervals

Results

765.0ms	8671×	body	80	valid
222.0ms	2667×	body	80	nan

Details

sample260.0ms

simplify272.0ms

prune6.0ms

localize24.0ms

rewrite19.0ms

series64.0ms

simplify84.0ms

prune166.0ms

localize25.0ms

rewrite16.0ms

series64.0ms

simplify108.0ms

prune218.0ms

localize26.0ms

rewrite17.0ms

series64.0ms

simplify114.0ms

prune206.0ms

localize31.0ms

rewrite17.0ms

series62.0ms

simplify68.0ms

prune420.0ms

regimes254.0ms

bsearch73.0ms

simplify3.0ms

end0.0ms

sample1.4s

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